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Wednesday, December 18, 2013

Joanna's Percent Post

What is a percent?

Percent is an equivalent fraction out of 100.
Here is how we find an equivalent fraction out of 100.

  9/10 = 90/100
  9 x 10 = 90                 Why 100%? 100 is used because it's just right. It is also a number that is
  10 x 10 = 100                                                            easily seen.

Percent was made by the French. Per means 'out of' in French and Cent means '100'. Together, they make 'out of 100'. For the percent symbol %, the line symbolizes the 1 while the two little circles represents the two zeros from 100.

Improper or Top Heavy fractions are fractions that have a greater numerator than the denominator.
205/100 = 2 wholes, 205 out of 100, 205%
5/4 = 5 out of 4, 125 out of 100, 125%

100% means all, whole, everything, 100/100, 6/6.
10% means 10/100, 1/10.
50% means half, part / whole, 20/40 or 50/100.
25% means 25/100, 1/4, one quarter.
1% means 1 out of 100, 1/100.

Representing Percents %

a) 180%

                                         












b) 0.6%


c) 12 3/8%



Fractions - Decimals - Percents

Fractions and converting them into decimals and percents...

1) 3/40 

Decimals: ÷ 40 = 0.075

Percents: 0.075 x 100 = 7.5 

               0.075    /     1
       0.075 x 100 / 1 x 100
                7.5    /    100

3/40 --> 0.075 --> 7.5/100

Decimals and converting them into fractions and percents...

2) 0.086

Fractions:               43 / 500 
                                How?
                         0.086 / 1
            0.086 x 1000 / 1 x 1000
                            86 / 1000
                     86 ÷ 2 / 1000 ÷ 2
                          43 / 500


Percents: 43 ÷ 500 = 0.086 0.086 x 100 = 8.6%


0.086 --> 86/1000 or 43/500 --> 8.6%

Percents and converting them into decimals and fractions...

3) 33%

Decimals: 33 ÷ 100 = 0.33

Fractions:     33 / 100
                       How?
                 0.33 / 1
      0.33 x 100 / 100
                  33 / 100

33% --> 0.33% --> 33/100




PERCENT OF A NUMBER

                  1) 20% of 60

Calculator: 20 ÷ 100 = 0.20                            Mental Math:    |  %   
0.20 x 60 = 12                                                                           60 | 100  
                                                                                      ÷ 5       12 | 20    ÷ 5
20% of 60 = 12                                                                     12% of 60 = 12

A way of finding a percent of a number is to divide. Of means divide. In other words, you are multiplying 20% to 60, but what is 20% as a number? In order to do that, you have to divide your percent by 100. After that, you multiply your decimal to your number or whatever amount you have.

               2) 0.1% of 40

Calculator: 0.1 ÷ 100 = 0.001                         Mental Math:    #   |   %
0.001 x 40 = 0.04                                                                      40  | 100               
                                                                                ÷ 1000    0.04  | 0.1   ÷1000       
                                                                                             0.1% of 40 = 0.04

Since 0.1% is less than 1 and you know that 1% of 40 is 0.40, you should have something that is less than 0.40.
When dividing by 10, 100, 1000, etc, you move the decimal to the left by how many zeros are in the number. 
60 ÷ 100 = 0.60
          6 0 . 0 = 0.60
                                                                            ^ ^ ^   - move to two place values since 100 has 2               
                                                                                                                 zeros.

                3) 250% of 400

Calculator: 250 ÷ 100 = 2.50                           Mental Math:    #  |   %  
2.5 x 400 = 1000                                                                      400 | 100
                                                                                       x 2     800 | 200   x 2
                                                                                      ÷ 4     200  | 50     ÷ 4
                                                                                            + 1000 | 250
                                                                                        250% of 400 = 1000

Since 250 is greater than 100, you'll end up having more than you total.
             What you do on one side, you do to the other.

Combing Percents %

When you are working with money, you may often see discounts, sale prices, or regular prices...

Discount - What you save
Sale Price - What you pay

When finding the sale price...

Regular Price - Discount = Sale Price

When finding the total price including the taxes...

Step 1) Calculate the total prices of the item(s) that were bought.

4.4 Page 149

7.  A herd of 100 caribou moved to a new location. The population increased by 10% the first year and then increased by 20% the second year.
             a) Find the population after the second year.
             b) Explain why there was not a 30% increase in population over the two years.

             a) The population of the herd of caribou was 132. How?

                                

  1. For finding the increase of the caribou, first thing's first is to add 100 + 10 since 'increasing' means to end up having more than what you had before. This tells you that for your answer, you should have a number that's more than the regular amount of caribou. 
  2. After that, you need to take the percents that were from the question and convert them into a decimal. By doing so, you would have to divide the percent by 100.
  3. Last part is to multiply the decimal to the total amount of caribous.

                            100 + 10 = 110                 110 ÷ 100 = 1.10              1.10 x 100 = 110


                                100 + 20 = 120              120 ÷ 100 = 1.2            1.2 x 110 = 132

                     b) The reason why 30% was not used because 100% was changed. From the first photo, the total amount of caribou were 100, but since we needed to make another diagram, the total was not 100 anymore because it was changed to 110 instead.

4.4 Page 148 Show you know

What is the final sale price at each store? Which is a better buy? Explain your thinking.

Store A: 50% off one day only
Store B: 25% off one day followed by 25% off the reduced prince the second day

Store A:

Price - $200 for a guitar
200 ÷ 2 = 100
Why 2? I used 2 because the 2 represents half of the number and in decimals, half equals 0.5.
or
50 ÷ 100 = 0.50              0.50 x 200 = 100 
The final price of the guitar in Store A is $100.

Store B:

Price - $200 for a guitar

25 ÷ 100 = 0.25       0.25 x 200 = 50        200 - 50 = $150 
   25 ÷ 100 = 0.25         0.25 x 150 = 37.5        150 - 37.5 = $112.50
First, you'll need to convert your percent, in this case it is 25%, to a decimal. In order to do that, you'll need to divide your percent out of 100 since percentage is out of 100%. 

25 ÷ 100 = 0.25

Second, you will need to solve what 25% is out of 200. To do that, you need to multiply the decimal to the total which is 200.

0.25 x 200 = $50

Now, you have found what 25% is out of 200 but you do not know how much you pay. Since we are working with money, 25% is what you save. You aren't done till you have your sale price. To find your sale price, you need to subtract 25% of 200 from $200.

200 - 50 = $150

You now have the sale price of the guitar of that one day. Next step is to find another 25% off from the sale price on the second day.

Again, you'll need to convert the percent into a fraction and multiply the given decimal to the sale price, which is 150.

25 ÷ 100 = 0.25                     0.25 x 150 = 37.5 or $37.50 

After that, you will need to subtract 25% of the reduced price and subtract it from the sale price, $150.

150 - 37.5 = 112.5 or $112.50

Which is a better buy? Buying the guitar from Store A is a better buy because you are saving $12.50 if you don't buy it from Store B. The reason why Store A was better than Store B was because of how the total of 100 was changed to 150 which caused it to have a bigger amount. Since Store B has a greater total or all than Store B, it will end up saving less than what Store A is saving.

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